Study of Capital Asset Pricing Model in
Nordic Stock Market
Nupur Garg
Master’s thesis November 2019 School of Business Master’s Degree Programme in International Business Management
Description
Author
Garg, Nupur Type of publication
Master’s thesis Date
November 2019
Language of publication: English
Number of pages
59 Permission for web
publication: Yes
Title of publication
Study of Capital Asset Pricing Model in Nordic stock market
Degree programme
Master’s Degree Programme in International Business Management
Supervisor(s)
Hundal, Shabnamjit
Assigned by
JAMK Centre for Competitiveness
Abstract
This study focused on studing the impacts of using CAMP in estimating the
performance of the Nordic stock market. Random sampling was used and a total of
35 companies were selected for the case study. CAPM formula, as formualted by
previous studies, was used to estimate the performance of these companies and
various anayses has done on the data including regression, t-test and Jensen alpha
tests.
From the descriptive statistics, it was found that the average beta was 0.0191 while
the maximum beta was 0.759. This implies that the selected Nordic stocks had a
systematic risk of 99% lower than the index. Further, Jensen Alpha analysis showed
that the Nordic stock has outperformed the market’s expected return based on
CAPM productions. However, looking at the t-test values, there has been a
significant change in the systematic risk in Nordic stocks and at the same time, there
has been a significant change in the unsystematic risk of this market. The regression
analysis shows that there was a positive association betwen beta and daily returns
with an increase in beta leading to a possible increase in actual return. Therefore, the
finding was not statistically significant. The expected return was also calculated.
The finding showed that beta is not the only factor to be considered when making
investments in the Nordic stock markets.
In conclusion, the study finds that CAPM is not an accurate model to be used in
measuring the expected returns of investments in the Nordic markets.
Keywords/tags
Risk and return, CAPM, Jensen Alpha, Regression, t-Test, Nordic stock market Miscellaneous
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Contents
1. INTRODUCTION ...................................................................................................... 4
1.1 Background ...................................................................................................... 4
1.2 Research Objective and Questions .................................................................. 6
1.3 Motivation for the Research ............................................................................ 7
1.4 Structure of the Thesis ..................................................................................... 8
2. THEORETICAL BACKGROUND ................................................................................. 9
2.1 Introduction ..................................................................................................... 9
2.2 Return .............................................................................................................. 9
2.3 Risk ................................................................................................................ 10
2.3.1 Types of risk...............................................................................................10
2.3.2 Systematic and Unsytematic risk..............................................................11
2.3.3 Standard deviation....................................................................................11
2.4 Beta ................................................................................................................ 12
2.5 Capital Asset Pricing Model (CAPM) ........................................................... 13
2.6 Jensen Alpha .............................................................................................. 16
2.7 Summary ................................................................................................... 17
3. EMPIRICAL LITERATURE REVIEW .......................................................................... 18
3.1 Introduction ................................................................................................... 18
3.2 Empirical Literature Against CAPM ............................................................. 18
3.3 Empirical Literature Supporting CAPM ........................................................ 20
3.4 Chapter Summary .......................................................................................... 22
4. RESEARCH METHODOLOGY .................................................................................. 23
4.1 Introduction ................................................................................................... 23
4.2 Research Approach ........................................................................................ 23
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4.3 Context of study ........................................................................................... 24
4.4 Sampling and Data Collection.......................................................................27
4.5 Variables .................................................................................................... 28
4.6 Data Analysis ............................................................................................ 31
4.6.1 Time series regression...............................................................................31
4.6.2 Cross-Sectional Regression .................................................................... 32
4.6.3 t-Test for Difference in Means ............................................................... 34
5. FINDINGS .............................................................................................................. 35
5.1 Introduction ................................................................................................... 35
5.2 Descriptive Statistics ..................................................................................... 35
5.3 Nature and Extent or Risk ............................................................................. 36
5.4 Jensen Alpha .................................................................................................. 37
5.5 Findings of t-tests .......................................................................................... 37
5.6 Cross-Sectional Regression: Relationship between Risk and Return ........... 38
5.6.1 Expected Return and Beta ...................................................................... 38
5.6.2 Expected Return, Beta, and Residual Variance ...................................... 40
5.7 Chapter Summary .......................................................................................... 41
6. CONCLUSION AND RECOMMENDATION .............................................................. 42
6.1 Conclusion .................................................................................................... 42
6.3 Summary and Discussion..............................................................................43
6.3 Limitations of the Study ................................................................................ 45
6.4 Recommendations for Future Research ........................................................ 45
7.REFERENCES .................................................................................................... 47
Appendix
Appendix 1. Information on Swedish Companies.......................................................53
Appendix 2. Information on Danish Companies.........................................................56
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Appendix 3. Information on Finnish Companies..........................................................57
Figures
Figure 1. Composition of Total risk............................................................................36
Tables
Table 1. Probability of each scenario with certain rate of return...............................11
Table 2.1 Nasdaq Nordic & Baltic growth between 2014 and 2018..........................25
Table 2.2 number of companies in Nasdaq Nordic & Balticby sector........................26
Table 2.3 List of companies selected for the study .....................................................27
Table 2.4 Definition of Key variables..........................................................................30
Table 3 Table of Findings.............................................................................................
Table 3.1 Descriptive statistics...................................................................................35
Table 3.2 t-test output.................................................................................................37
Table 3.3 Regresion model of return and beta...........................................................38
Table 3.4 Regression model of return, beta and residual variances...........................40
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1. INTRODUCTION
Capital Asset Pricing Model (CAPM) is one of the most significant concepts in
finance. The model argues that the required return on asset is influenced by its
systematic risk. The model is applied in estimating returns on assets, including
stocks. However, several researchers have argued that the CAPM does not
hold in stock markets. This thesis examines the relationship between risk and
return of Nordic stocks, thereby assessing the validity of the CAPM in the
Nordic Stock Market. It analyses the returns on 35 stocks to determine whether
the Nordic Stock Market has underperformed or outperformed, based on the
CAPM expected returns. It also tests whether systematic risk of Nordic stocks
has changed between 2009 and 2019.
1.1 Background
The primary motivation for most investors is making a return on their
investments. Nearly everything an investor doesin relation to their investment
is geared towards ensuring that an investment that is making profits continues
to make the same profit at the very least, and if possible, that the investment
starts to make even more profit. By the same token, investors are as well likely
to divest away from an investment if it is only returning losses with no
potential for profit. While, it is clear what investors hope for, the reality is that
some investors still make losses sometimes, even if this is not what they hoped
for. Markowitz (2016) argues that his happens because of the challenges
associated with making predictions about future profits. While technologies,
historical financial data analysis skills, and investment models can be used to
predict the behavior of stocks, the risks of losses cannot be eliminated entirely.
Thus, investors always have to accept some level of risk when making their
investments.
The question therefore shifts from whether the investor can eliminate all risks
while making investment decisions, to how the investors can manage the risks
associated with their investments.
By shifting the question, the focus therefore turns to the relationship between
risk and return, a concept that has been examined at length by both scholars
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and investors. Brealey, Myers and Allen (2011) rightly points out that risk-
return relationship is one of the most significant aspects considered in various
investment decisions. According to Gitman, Joehnk & Smart (2015), the risk
associated with an investment determines the investor’s expected return,
whereby the higher the risk, the more chances are of a higher return. This is
the basis of the tradeoff theory, and what this means for investors is that they
always have to choose between the two conflicting goals: minimizing risk
ormaximising returns. Brigham & Houston (2016) further notes that most
investment managers know this, and for that reason, they employ the use of
various models to help predict the estimated risks and the expected returns of
their portfolio. One popularly used model is the capital asset pricing model
(CAPM).
The CAPM is applied in determining the relationship between risk and return
on an investment. According to Watson and Head (2016), unsystematic risk is
ignored in portfolio management and other investment decisions, since it can
be eliminated through diversification. The concept of CAPM is also applied in
estimating the cost of capital, which is used in investment appraisal decisions.
This is vital in assessing the viability of projects using the net present value
(NPV) criterion. Long-term investments such as purchase of fixed assets,
expansion, and introduction of new products, among others are appraised using
NPV. The NPV discounts all the expected cash flows at the company’s cost of
capital.
The CAPM lays the foundation for the relationship between risk and return
(Brealay, Myers, and Allen 2011). It argues that investors are risk-averse and
require a higher return on an asset associated with a high risk. It implies that if
an investment has a high risk, it must generate a high return to attract
investors. The CAPM posits that risk can be divided into systematic and
unsystematic risk. Systematic risk relates to market-wide factors and cannot be
eliminated by diversification, while unsystematic risk is due to firm and
industry-specific factors. Systematic risk is measured by beta, which measures
an asset’s risk relative to the market risk. The model assumes that investors
can eliminate all the unsystematic risk by establishing well-diversified
portfolios. Therefore, they base their investment decisions solely on systematic
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risk. The model is widely used in estimating required returns on stocks and
other investments. This thesis investigates the relationship between risk and
return of Nordic stocks to assess the validity of the CAPM. It also uses the
CAPM to compare the performance of the Nordic stocks with the CAPM’s
estimated required returns.
Despite is usefulness, questions have emerged regarding the usefulness of
CAPM to predict the relationship between risk and return, with some
researchers concluding that it does not offer any meaningful estimations of risk
and return. The CAPM assumes that returns on an investment depend on the
investment’s systematic risk since unsystematic risk is irrelevant in investment
decisions. However, various researchers have questioned the validity of
CAPM and challenged its application in pricing assets. For instance, Dempsey
(2013) argues that the empirical evidence against CAPM is so compelling that
the model should be abandoned. Östermark (1991) also found evidence against
the validity of CAPM in the Finish and Swedish stock markets. The conflicting
findings in the various studies that exist so far make it a challenge for
managers and investors to know whether CAPM can benefit them or not.
Beyond the conflicting findings, fewstudies discuss the significance of CAPM
within the Nordic Stock Market, which lead to information gap. This
background show why a furtherstudy of CAPM and its usefulness in the
Nordic Stock Market is important.
1.2 Research Objective and Questions
The goal of this research is to determine whether CAPM beta (systematic) and
total risk explain the cross-section variation in returns on stocks listed on the
Nordic Stock Market. To achieve this goal, the following research questions
have been deduced:
i. What is the nature and extent of risk in the last 10 years?
ii. Has the Nordic stock market underperformed or outperformed the
expected return (CAPM) in the last 10 years?
iii. Is there any change in systematic, unsystematic and total risks in
Nordic stock market in the last 10 years between 2009 and 2019?
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iv. What is the relationship between risk and return of stocks listed on
the Nordic Stock market?
In the first question, CAPM is used to estimate beta and calculate systematic
risk. This will help determine the proportion of total risk (standard deviation)
that is accounted for by systematic and unsystematic risks. For the second
question, Jensen alpha is used to determine the difference between the actual
returns on the stocks and the estimated required returns (CAPM returns).
Studying the relationship between risk and return helps determine whether the
CAPM is valid or not.
1.3 Motivation for the Research
This study is motivated by two reasons, one being a practical justification, and
the second being a theoretical justification. The theoretical justification is
inspired by the gaps observed in the extent studies as shown in the
background. As it is, a number of studies have shown that CAPM can be used
to help in estimating risk and return. At the same time, contrasting studies have
shown that CAPM is not a sufficient approach to estimate risk and return.
Thus, by making an additional study, a review of extant literature is made,
which critically examines the findings of previous studies and makes a critical
review why CAPM is considered inadequate. The study also presents an
updated review of literature, which is far from the authority in the subject, but
provides a relevant additional information to both researchers and students of
finance management. However, CAPM is a major area of finance which helps
investors to know the risk and return. According to ACCA (2019), CAPM was
published by William Sharpe in the year 1986. Watson & Head (2016) states
that unsystematic risk can be ignored but systematic risk plays a very
important role.
Secondly, on a practical level, the resulting controversy on the significance of
CAPM makes it harder for managers to make decisions on whether they will
adopt the model when making their investment decisions. This thesis may
contribute to the knowledge necessary in making investment decisions as it
focuses specifically on the relationship between risk and return on Nordic
stocks to assess the validity of data. The research determines whether CAPM
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beta is a significant determinant of the variations in cross-section returns of the
Nordic stocks using more recent data from 2009 to 2019. The findings of this
thesis can help investors and companies listed on the stock markets of Finland,
Denmark and Sweden to better understand the relationship between risk and
return.
1.4 Structure of the Thesis
The study is organized into six different chapters. Chapter one discusses the
background, aims, and objectives, as well as the justification for studying the
CAPM in the Nordic Stock Market. Chapter two reviews theoretical
background of CAPM, including its assumptions and its limitations. Chapter
three reviews empirical studies on the CAPM and relationship between risk
and return, identifying gaps in research. Chapter four of the study explains the
research methodology, including a description of the data used and how it is
collected, as well as a discussion of the statistical methods applied. The
chapter also includes a justification for the models used. Chapter five presents
the findings of data analysis, implications of the findings, and links to findings
to existing empirical studies. Finally, Chapter six is conclusion of the study,
including a summary of the research, limitations of the study, and areas for
further research.
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2. THEORETICAL BACKGROUND
2.1 Introduction
This chapter discusses the theoretical literature on CAPM and the relationship
between risk and return. The first section, theoretical background, defines
return, risk, CAPM, expected return and Jensen alpha. The section also
highlights the different types of risk, as well as measures for risk and return.
2.2 Return
Brealey, Myers and Allen (2011) define return as the profit or loss on any
investment activity. Return includes profit, interest, or dividend earned on an
investment, plus capital gains (Watson & Head, 2016). Capital gain or loss
refers to the change in the value of the investment over a period. Mayo (2012)
identifies three types of return; realized, expected, and required returns.
Realized return is the measure of how much an investor has gained or lost on
an investment over the period the investment was held. The realized return on
a stock is calculated as follows:
Realized return = (Ending Price−Initial Price)+Dividends
Initial Price × 100%
Expected return is the gain or loss an investor anticipates from an investment,
based on its historical performance (Mayo 2012). For instance, the expected
return on a stock is the historical average return of the return. Under
uncertainty, the expected return is calculated as follows:
Expected return =∑ 𝑅𝑖𝑃𝑖, where Ri is the return and Pi is the probability of the
condition.
Required return is the minimum return expected on an investment. It is the
opportunity cost of capital, that is, the amount an investor would earn on other
available market securities. According to Gittman and Zutter (2015), a rational
investor cannot commit on an investment if its expected return is lower than
the required return. In efficient markets, the expected return is equal to the
required return (Ilmanen 2012).
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2.3 Risk
According to Yang (2014), the risk which is involved in an investment can
indirectly explained with some specific concepts.
2.3.1 Types of Risk
Risk- Here, in the case of investment, the return always remains uncertain
because nobody knows the situation of market as well as what will be the
situation in the future so there is always some risk involved in every kind of
investment. So, risk is all about the uncertainity available in the expected
return. Taking risk may lead to an opportunity as well as loss because no one
knows what will happen next. Accordingly, every investment involves risk
(Bodie et al. 2004).
Risk free- Risk free is a type of return in which investors get some return by
the end of their holding period. Here, government bond is also taken as risk
free assets due to the fact that government always print money and this is
helpful for the investors as they get assured about their investment. Investors
need to give some amount in advance so that they will get that amount back at
the end of period (Sibilkov 2007).
Risk premium- Risk premium is all about the compensation involved in the
investment. This can be measured by the rate of return earned by having the
investment from the excess of risk free ROR (Drobny 2010).
Therefore, risk refers to the variability or volatility of returns associated with
an investment (Markowitz 2016). Due to changes in the firm’s operating
conditions, sector and market factors, an investment may not generate the
expected return (Markowitz 2016). Therefore, investment decisions must
consider both expected returns and risk.
The total risk associated with an investment is measured using the standard
deviation. Standard deviation is measure of the variability of returns from the
mean return (Watson & Head 2016). It is determined by getting the square of
variance as follows:
Var(r) =∑ (𝑟𝑖 − 𝜇)2𝑛1 , where ri is the return and μ is the mean or average return.
Standard deviation = √𝑉𝑎𝑟(𝑟)
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2.3.2 Systematic and Unsystematic return
According to Markowitz (2016), total risk is divided into systematic and
unsystematic risk, depending on the contributing factors.
Total Risk = Systematic Risk + Unsystematic Risk
Unsystematic risk: It the risk inherent in a specific firm or industry(Moyer,
McGuigan & Kretlow 2005). It is due to factors such as employee strikes,
government policy specific to a sector, firm’s financial challenges, and
unavailability of raw materials, among other firm-specific factors. It is also
called diversifiable risk since it can be eliminated through diversification.
Systematic Risk: It is the proportion of total risk that is inherent in the entire
market. It is due to market-wide factors and affects all firms or investments
irrespective of the sector (Moyer et al. 2005). Causes of systematic risk include
changes in interest, inflation, exchange rates, among other market-wide factors
(Moyer, et al. 2005). Such factors are beyond the control of a firm or investor.
Thus, unsystematic risk cannot be eliminated through diversification (Watson
& Head 2016). According to Markowitz (2016), unsystematic risk can be
eliminated through diversification, hence investors base their decisions on
systematic risk. Systematic risk is measured using beta.
2.3.3 Standard deviation- A Measure of Risk
Bodie at al. (2004) discussed that while making a decision to invest or not, an
investor has to take the possible outcomes of investing in current scenario and
also HRP stocks in the current scenario. After that, he also needs to caculate
the estimated probability of every scenario.
Table 1- Probability of each scenario with certain rate of return [Accessed
from Bodie at al. (2004)]
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Here, an example is taken in the above table where s denotes the number of
scenario. The statistical measurement of expected risk and return is presented
in the above table of probability distribution. According to the table, HRP is
equal to the return on the investment which is expected.
E(Rt)=RtPs where,
Rt denotes realized return of every single stock.
Variance is used to measure the volatility of the realized return. This is helpful
in calculating or estimating the uncertainty of the risk. In addition to that, we
take square root of variance for calculating the standard deviation so that the
risk taken from expected return must have the same dimensions.
However, for calculating the stock performances, standard deviation and the
expected return are the major parameters (ibid).
2.4 Beta
Beta is a measure of an investment’s volatility relative to that of the entire
market (Lumby & Jones 2003). For instance, if a stock’s beta is 1.2, it implies
that the volatility of the stick’s returns is 20% greater than that of the market.
On the other hand, a beta of 0.8 implies that the stock’s risk is 20% lower
than that of the market. This also implies that if the market volatility increases
by 1 unit, the stock’s risk will increase by 0.8 (Lumby & Jones 2003).
Beta is calculated by determining the covariance between the stock’s return
and the index or benchmark’s return divided by the variance of the
benchmark’s return (Lumby & Jones 2003). Alternatively, it be estimated by
getting the regression of a stock’s returns on the benchmark’s return (Lumby
& Jones 2003). It is the coefficient of the benchmark’s return in the regression
model.
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Beta, β = 𝐶𝑜𝑣(𝑟𝑖,𝑟𝑏)
𝑉𝑎𝑟(𝑟𝑏), where ri represents the stock’s returns and rb returns on
the benchmark.
2.5 Capital Asset Pricing Model (CAPM)
CAPM explains the relationship between return and risk. The model was
introduced by Jack Treynor in 1961 to help in pricing assets (Brealey, Myers
& Allen 2011). The model states that securities are priced commensurate with
a trade-off between un-diversifiable/systematic risk and expectations of return
(Dempsey 2013). This implies that investors consider the systematic risk
associate with a security to determine the expected return and price of the
security. The model further provides that the required return on a portfolio or
asset is based on the asset’s systematic risk (beta) and the market risk
premium (Brigham & Houston 2016). The difference in between the market
return and the risk-free rate is known as market risk premium.
Required return, Ri = Risk-free rate + Beta × (Market return – Risk-free rate)
The risk-free rate is the return on assets considered risk-less such as
government bonds and securities. Beta is the measure of a security’s
systematic risk, that is, the volatility of its returns relative to that of the
market (Brigham & Houston 2016). The market return is the return on the
entire market. Returns on various market indices such as the OMX Nordic 40
are often used as the proxies for market return.
CAPM is based on the following assumptions:
1. The model assumes that all investors are risk-averse and rational.
Risk-averse investors are those that only accepts additional risk on an
investment if the investment provides an additional return to
compensate the risk (Fabozzi& Ake 2013). Therefore, investors
require an additional return over and above the risk-free rate. It
implies that the greater the asset’s volatility, the higher the return the
investors will require on the asset (Brigham & Houston 2016). Thus,
there is a linear positive association between risk and return.
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2. CAPM also assumes that all investors aim to maximise utility
(Fabozzi & Ake 2013). This implies that one given two or more
options, an investor would select the security that maximise return at
every level of risk.
3. The model further assumes that the markets are efficient and investors
have all the information about securities (Brigham & Houston 2016).
In efficient markets, asset prices reflect all information about the
securities. Assets in efficient markets are correctly priced hence an
investor cannot outperform the market by applying fundamental and
technical analysis to predict future price movements and identify
underpriced securities (Brigham & Houston 2016). Besides, market
efficiency implies that there are no transaction costs, taxes, as well as
restrictions on short selling (Fabozzi & Ake 2013).
4. A fundamental assumption of the CAPM is that investors base their
investment decisions on risk and return. The model further postulates
that beta is the only important measure of risk (Clayman, Fridson&
Troughton, 2012). This assumption is premised on the modern
portfolio theory which states that unsystematic risk can be eliminated
through diversification, and that the markets are efficient (Clayman, et
al. 2012). Market efficiency enables investors to create well-
diversified portfolios, thereby eliminating unsystematic risk.
5. Investors can lend and borrow unlimited amounts at the risk-free rate
of interest (Clayman, et al. 2012). This implies that there are securities
designated as risk-free. Thus, investors have an option of investing in
risk-free assets or in risky assets. For investments in risky assets,
investors require an additional return over and above the risk-free rate.
Government bonds and other securities are considered risk-free
(Guerard & Schwartz 2010).
6. The model also assumes that investors have similar expectations of
risk and return (Guerard & Schwartz 2010). This implies that the
estimates of risk and return are similar across all investors. This is
15
attributed to the fact that information is available to all investors in the
market (Clayman, et al. 2012). Therefore, all investors give a similar
estimate of the price of a security.
7. CAPM also assumes that investors have identical horizons
(Markowitz 2016). This implies that investors buy all securities and
sell them at one common point in time. Thus, the model assumes a
single investment horizon. This means that investors are only
concerned about the terminal wealth, that is, the value of the
investment at the end of the investment period.
8. Finally, the model assumes that all securities are marketable and
highly divisible (Markowitz 2016). This indicates that it is possible for
an investor to buy or sell any security at any time they wish.
The CAPM has been criticized for its theoretical limitations. According to
Brigham and Houston (2016), CAPM is based on unrealistic assumptions. For
instance, the assumption of a single period investment horizon is unrealistic.
Investors are not only concerned about the terminal value of their investments.
In reality, most investors have continuous investment horizons. Besides, the
assumption that all investors have similar expectations of risk and return is
unreasonable. Investors have different expectations of the market (Kurschner
2008). This is due to the fact that markets are not perfectly efficient.
Information is not available to all investors. This explains why some investors
outperform the market by incurring efforts and resources to obtain information
that is not readily available, through measures such as technical and
fundamental analysis (Peterson 2012). The assumption that investors can
borrow and lend unlimited amounts of money at the risk-free rate of interest is
also unrealistic (ibid.)
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2.5 Jensen Alpha
Jensen alpha, is also known as Jensen measure, was introduced in 1968 by
Michael Jensen (Peterson 2012). It is used to assess the performance of a
stock or portfolio against the market or the CAPM required return (Guerard &
Schwartz 2010). It is the difference between the actual return and the CAPM
required return.
Where Ri is the actual return on the portfolio or stock, Rf is the risk-free rate,
β si beta, and Rm is the market or index return.
The sign of the Jensen alpha indicates whether an investment has
underperformed or outperformed the market. If it is positive, it indicates that
the investment’s actual return is greater than the risk-weighted expected
return (CAPM return). This implies that the investment has outperformed the
theoretical expected return. It means that the investment has delivered a
higher return than what it beta suggests. However, if the Jensen alpha is
negative, it indicates that the actual return on the investment is less than the
theoretical expected return. This shows that the investment has
underperformed the market. Since the required return is based on beta, a
negative alpha suggests that an investment has not delivered sufficient returns
to commensurate its systematic risk.
According to Brigham and Houston (2016), Jensen alpha is used to evaluate
the performance of portfolio or investment managers, as well as the allocation
of funds to portfolios. This is because it reflects the future performance of the
portfolio or investment. When comparing two or more investments, the one of
the highest Jensen alpha is considered to have outperformed the other
investments. Therefore, a portfolio with the highest Jensen alpha is allocated
more resources than those with negative or low Jensen alpha. An investor
would divest a portfolio or security if its Jensen alpha is negative since it
indicates that the return on the investment is not commensurate with its
systematic risk.
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2.7 Summary
The chapter reviewed theoretical and empirical literature on CAPM and the
relationship between risk and return (Fabozzi& Ake 2013). Risk and return
are fundamental measures investors rely on during investment decisions. Risk
refers to the variability of returns on an investment (Brigham & Houston
2016). Risk is classified into systematic and unsystematic risk depending on
the contributing factors. Systematic risk is due to market-wide factors such as
changes in interest rates, inflation, and exchange rates, among other variables.
Unsystematic risk is due to firm and sector-specific factors (ibid.)
Unsystematic risk can be eliminated by creating a well-diversified portfolio of
assets. Systematic risk is measured using beta, while total risk is measured
using standard deviation. Because unsystematic risk can be eliminated,
CAPM assumes that beta is the only determinant of stock and portfolio
returns (Fabozzi& Ake 2013). Modern portfolio theory provides a guideline
for reducing portfolio risk. It recommends that investors should create a
portfolio consisting of unrelated stocks, since the covariance between such
stocks is low. The theory suggests that investors can create an efficient
portfolio, or the minimum variance portfolio. This is the portfolio that
maximizes the risk-adjusted performance (Brigham & Houston 2016). Risk-
adjusted measures include Sharpe and Treynor ratios. Sharpe ratio shows the
excess return above risk-free rate per unit of standard deviation (Fabozzi&
Ake 2013). The chapter also discussed CAPM including its assumptions such
as existence of risk-free rate, similar expectations of risk and return, markets
are efficient, among other assumptions.
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3. EMPIRICAL LITERATURE REVIEW
3.1 Introduction
This section reviews the empirical literature on CAPM and the relationship
between risk and return. Empirical literature review is important since it
enhances understanding of the topic and enables the identification of research
gaps. It assists in developing hypothesis and determining the appropriate
methodology for future studies on CAPM.
After the introduction of CAPM, various empirical studies have been
conducted to determine its validity in stock markets. Most of the studies have
focused on one fundamental assumption of the CAPM, that is, beta is the only
determined of return, and that the relationship between beta and return is
linear. Based on this assumption, the regression model of return and beta
should be statistically significant. Besides, the intercept of the model should
not be significantly different from the risk-free rate.
3.2 Empirical Literature Against CAPM
Among the early empirical studies on the CAPM was conducted by Lintner.
Lintner used ten-year data on 301 stocks from 1954 to 1963. Lintner’s
analysis involved a two-stage regression analysis. The first stage was the time
series regression analysis conducted to estimate the beta of each asset. The
slope of the regression of the stock’s returns and the market returns gave an
estimate of beta. The second stage of the analysis involved a cross-section
regression of the 301 pairs of returns and beta. Lintner’s cross-sectional
regression model is shown by the following equation:
Ri = α0 + α1β + є
Lintner found that the intercept of the cross-sectional regression was
significantly different (greater) than the risk-free rate. Besides, the coefficient
of beta in the model was not statistically significant. Lintner concluded that the
analysis did not support the validity of CAPM.
Miller, Jensen, and Scholes (1972) analysed monthly data of all securities
listed on the NYSE from January 1926 to December 1930. They used time-
19
series regression to estimate beta for each of the stocks. They then divided the
sample into ten different portfolios based on beta values. Miller, et al. (1972)
then conducted two cross-sectional regressions. The first cross-section
regression was between portfolio returns and beta. In the second regression,
Miller, et al. (1972) added residual variance to the model. The results showed
that the R-square of the model increased when residual variance was added.
This indicates that beta is not the only determined of return, thereby
invalidating CAPM.
Levy (1978) used the same methodology as Miller, et al. (1972) analyzing
twenty-year data of 101 stocks. The r square of the model cross-sectional
regression with beta was 0.21, but when variance was added, the r-square
increased to 0.38. Levy (1978) concluded that the CAPM was not valid since
beta was not the only determined of return on stocks and portfolios. Fama and
French (2003) also tested the empirical validity of the CAPM and found no
empirical proof of CAPM assumptions.
Novak, and Petr (2004) studied the impact of CAPM beta, market value of
equity and momentum on stock return on the Stockholm Stock Exchange. The
study found that none of the factors, including CAPM beta is significant for
explaining stock returns on the Stockholm Stock Exchange. This suggests that
CAPM is not valid since it posits that CAPM beta is a significant and the only
factor explaining variability of stock returns.
Östermark (1991) used regression model to assess the relationship between
beta and stock returns in two Scandinavian Stock Markets; Sweden and
Finland. The study relied on the r-square (coefficient of determination) to
assess the explanatory power of squared beta. The study found that in the
Finnish Stock Market, the explanatory power of squared beta was low. The
model for the Swedish Stock market indicates that squared beta explained a
greater percentage of the variations in stock returns than in the Finnish market.
Östermark (1991) concluded that the Finnish model was consistent with
international evidence on the invalidity of CAPM.
Boďa and Kanderová (2014) used monthly data of 10 S&P 500 index stocks
from 2003 to 2012 to test the linearity of the relationship between CAPM beta
20
and stock returns. They divided the data into two subsequent non-overlapping
5-year sub periods. They used regression model to determine the relationship
between beta and stock returns. The study found that there is no linear
relationship between beta and stock returns. Besides, there was a significant
change in beta between the two sub periods. The results invalidate the linearity
assumption of CAPM (Boďa, and Kanderová 2014).
Anwar and Kumar (2018) tested whether the CAPM holds in the Indian stock
market, using data of NIFTY 50 companies from April 1, 2009 to March 31,
2016. The performed time-series regression to determine stocks’ betas and
cross-sectional regression to assess the relationship between beta and stock
returns. The data was subcategorized into portfolios based on size and value.
The regression models indicated that CAPM beta was not robust in explaining
stock returns of the NIFTY 50 companies. However, when portfolios were
used, the explanatory power of the CAPM beta improved although it was still
very low. Anwar and Kumar (2018) concluded that the CAPM did not hold in
the Indian stock market.
Karp and Van Vuuren (2017) studied the validity of CAPM and the Fama
French Three-Factor model in the Johannesburg Stock Exchange. Using data
of 46 companies listed on the JSE from 2010 to 2015, they constructed
portfolios using an annual sorting procedurebased on Size and Book-to-
Market. The study found that the models are poor in explaining stock returns.
However, Karp and Van Vuuren (2017) identified inadequate market proxy
measures as the primary reason for the poor performance of the models.
These findings suggest that CAPM is inadequate in being used as a proxy to
help improve returns to investors. Particularly, the studies looked at how the
model influences beta, stock’s returns and the market returnin various
marketsacross selected stock exchanges. They find that CAPM is not robust
enough to explain the returns earned, irrespective of the company or market in
question.
3.3 Empirical Literature Supporting CAPM
Although most studies have rejected the validity of CAPM, other studies have
supported the validity of CAPM and its application in estimating stocks’
21
returns. Fama and MacBeth (1973) studied monthly percentage returns of all
stocks listed on the New York Stock Exchange between January 1926 and
June 1968. They performed time-series regression on each stock to estimate
betas. They divided the data into 20 portfolios on the basis of ranked betas of
individual stocks, with each portfolio having equally weighted stocks. They
estimated the beta for each portfolio (equally weighted), residual variance and
squared beta. Fama and MacBeth (1973) then conducted cross-sectional
regression analysis with actual returns on each portfolio as the dependent
variable, while beta, residual variance and squared beta were the independent
variables. Analysis showed the intercept of the model was not statistically
significant. The coefficients of squared beta and residual variance were not
statistically significant, while the coefficient of beta was statistically
significant. They concluded that the regression showed that beta was the only
significant determinant of stock returns, thereby supporting the CAPM.
Sreenu (2018) tested the capital asset-pricing model (CAPM) and three-factor
model of Fama in Indian Stock Exchange. Using daily and annual average data
of 54 companies listed on the National Stock Exchange from 2010 to 2016,
they developed regression models for both the CAPM and Fama models. The
results showed that the intercepts of both models were statistically
insignificant (Sreenu 2018). This supports CAPM since an insignificant
coefficient implies that beta is the only factor explaining variability of returns.
Satrio (2015) tested the validity of CAPM and the Three-Factor model in
explaining returns of Indonesian stocks. Using data of 284 firms listed on the
Indonesian Stock Exchange from December 2002 to December 2012, he found
that CAPM is valid.
Roll (1977) provided a critique of the empirical tests that concluded that
CAPM is not valid and should not be applied in estimating returns. He argued
that the so called ‘empirical tests’ are invalid since they are based on
inefficient benchmarks. When estimating beta of a portfolio or stock, the
returns are regressed against the returns on a benchmark or market index.
CAPM requires such benchmark to be efficient. Roll (1977) also argued that
empirical arguments against CAPM are not valid from the theoretical and
practitioner’s view point. The fundamental principle of the CAPM is that
22
investors only consider systematic risk when determining returns since they
can eliminate unsystematic risk through diversification (Roll 1977). The
critique of CAPM that beta is not the only risk determining returns implies that
investors expected to be paid or compensated for unavoidable risk, an idea
which Roll (1977) finds inconsistent with the beliefs of theorists and
practitioners.
3.4 Chapter Summary
This chapter reviewed empirical studies that have been conducted to test
CAPM in stock markets. Most of these studies focused on the CAPM
assumption that beta is the only determinant of return. Empirical studies have
reached conflicting conclusions about the validity of CAPM in stock markets.
Miller, Jensen, and Scholes (1972), Levy (1978), and Boďa and Kanderová
(2014), among other studies found that CAPM does not hold in stock markets.
However, Fama, and MacBeth (1973), Sreenu (2018), and Satrio (2015) found
that CAPM is valid. The literature review shows that very few studies have
been conducted to test the validity of the CAPM in the Nordic Stock market.
This study uses the most recent 10-years data to test CAPM in the Nordic
stock market.
23
4. RESEARCH METHODOLOGY
4.1 Introduction
This chapter explains the research approach and strategy, data collection
method and variables used in the study. It also explains the statistical methods
employed to determine the relationship between risk and return, and test
CAPM.
4.2 Research Approach
Various research approaches can be used to conduct a study, and according to
one if the researcher, the choice of a particular approach over the other is
often pegged on how the researcher indents to treat truth and objectivity,
collect data, ananlyse the data and make inferences from the study. The
question of truth and how it is treated in a research is determined by the
research philosophy, of which there are positivism and interpretivism. On
research philosophy, this thesis is a positivism study. According to Wilson
(2019), a positivist research approach is a study in which the researcher is
independent and the findings can be considered objective. In this case, the role
of the researcher is restricted to collecting data and interpreting the results of
data analysis. The data used in the analysis is secondary data (stock prices),
which the researcher has no control over. The main strength of a positivist
approach over interpretivism is that it maintains objectivity where
interpretivists treat data with a subjective view, thereby leading to research
biases.
Trochim (2005) outlines two types of logical reasoning in research: inductive
and deductive. The key differences between them is that inductive techniques
focus on generating new theory and thought, whereas deductive reasoning
focus on testing the existing thought or theory to see its applicability within a
given context.A deductive approach implies that the aim of the study is to test
hypothesis about existing theories and not to develop new theories (Trochim
2005). The study adopts a deductive approach for two reasons. First, as
outlined in chapter one, this study aims at finding out whether CAPM beta
(systematic) and total risk explain the cross-section variation in returns on
stocks listed on the Nordic Stock Market. CAPM is an existing theory, which
means the use of a deductive approach to examine it is appropriate. Secondly,
24
this study focuses on a specific context, rather than just examining the theory
in a broad spectrum. Particularly, in this case, the hypothesis tested is whether
CAPM is valid in the Nordic Stock Exchange.
Another important methodological consideration was the research strategy.
According to Mc Burney and White (2013), research strategies can be
categorized into many brackets, the main ones being case studies, surveys,
experiments and field excursions. In the present case, case study is the
preferred strategy. Case studies refer to a research in which the goal is to look
at a specific organisation, country or segment of the market with the goal of
understanding how a phenomenon influences that selected entity based on its
unique characteristics. The strengths of conducting a case study is that the
findings are often specific to the context, making it relevant for
recommendations to be drawn and implemented from them. He also points out
that using a case study approach limits the ability to generalize findings.
Nevertheless, by using the case study approach, this study can focus
particularly on the Nordic stock market, which is where the research interest is
situated (ibid.)
Finally, this thesis uses a correlational research design. According to Mc
Burney and White (2013), a correlational research design involves determining
the relationship between two variables using quantitative data. The variables in
this study are numerical, making it possible to conduct a correlational
(quantitative) research.
4.3 Context of the study
As mentioned, the study is based on the Nordic stock markets. Before
describing the sampling and data collection procedures, it is imperative to
situate the study within the context. Nordic countries refer to countries situated
within a specific geographical region of North Atlantic and Northern Europe,
and typically comprise Sweden, Norway, Iceland, Denmark, Finland,
Greenland and Faroe Islands (Gotz 2003).The financial services and
marketplaces for this region is controlled by the Nasdaq subsidiary, Nasdaq
Nordic, which also controls the Baltic and the Caucasian regions.
25
Nasdaq Nordic was formed in 2003 as OMX AB, when HEX plc merged with
OM AB. It was renamed to Nasdaq AB, although it is also known as OMX AB
since February 2008 (Bakie 2014). Nasdaq Nordicoperates two divisions,
which control eight exchanges. These include Copenhagen, Stockholm,
Helsinki, Iceland, Tallinn, Riga, Vilnius, and Armenian stock exchanges. It is
one of the larger Nasdaq subsidiaries in Europe based on key statistics.
Specifically, as of end of year 2018, the daily average traded in Nasdaq Nordic
was 3.10 billion EUR.
The stock market has seen growth across most of its indicators. According to
its annual trading statistics report, average trades per day grew by 13.4% in
2018, while derivatives grew by 4%. However, the number of new companies
listed in Nasdaq Nordic declined significantly, from 118 to 84 between 2017
and 2018, although this is due to switches of where some 23 companies were
listed during the period (Nasdaq Nordic 2019).Nevertheless, the total number
of listed companies in the Nasdaq Nordic continued to grow, jumping from
792 to 10002 between 2014 and 2019. Table 2.1 is a summary of the growth in
number of listed companies in the Nasdaq Nordic and Baltic as reported by
Nasdaq, while Table 2.2 is a summary of the main sectors within the market,
together with the number of companies represented for each market.
Table 2. 1: Nasdaq Nordic & Baltic growth between 2014 and 2018
Year end Total Number of Listed Companies
2014 792
2015 852
2016 900
2017 984
2018 1,002
26
Table 2.2. number of companies in Nasdaq Nordic & Balticby sector
Industry/ sector Companies per ICB Sector
Oil & Gas 27
Basic Materials 47
Industrials 238
Consumer Goods 113
Health Care 149
Consumer Services 102
Telecommunications 15
Utilities 13
Financials 178
Technology 120
Total 1002
Notably as well, one of the main indices for the Nasdaq Nordic is the OMX
Nordic 40 (OMXN40), which was formed in 2006. The index consists of 40
most traded stock classes under the OMX Nordic umbrella in four markets,
which are Stockholm, Reykjavik, Helsinki and Copenhagen.
This context is significant for the study because Nasdaq Nordic is one of only
two pan-European stock exchanges active today. Further, it is larger than the
fellow Euronext by number of European markets represented in the listings.
By using Nasdaq Nordic, the study is able to find the most reliable data for the
selected study objective.
27
4.4 Sampling and Data Collection
According to Silverman (2010), it is advisable to work with a representative
sample where the population being studied is too large to be used in its
entirety. The context discussed above comprised more than a thousand
companies, which is too large for the scope of this study. This calls for
sampling techniques that are both useful and suitable for the particular study
based on factors such affordability, timeliness, efficiency as well as relevance.
In this case, random sampling is found to be the most suitable. Yin (2003)
defines random sampling as the procedure for selecting participants in a study
whereby any sample is selected purely based on chance, and the probability for
selecting a sample is equal for all the samples.
A random sample of 35 companies was selected from the list of companies
traded on the Nordic stock markets; Finland, Denmark and Sweden. A random
sample is beneficial in research since it eliminates sampling bias that affects
the objectivity of the findings. Close market prices of each of the 35 selected
companies and the OMX Nordic 40 Index were collected for the ten years
between 1 April 2009 and 31 March 2019. The daily stock prices were
collected since the variable is critical in the determination of stocks’ returns, a
key variable in this analysis. All the data was obtained from the OMX Nordic
website.
Table 2.3 shows the selected companies and the countries from which they are
selected. In summary, six companies were from Finland, eight were from
Denmark, and 21 were from Sweden.
Table 2.3: List of companies selected for the study as follows-
Company name Country Total per country
ABB LTD
Alfa
ASSA Abloy
Atlas copco A
Astra zeneca
Boliden
Electrolux B
Ericsson B
Sweden 21
28
Hexagon B
H&M
Investor B
Nordea bank
Sandvik
SEB A SV.Handelsbanken A
SKF
Swedbank A
Swedish Match
Tele 2 B
Telia company
Volvo B
Carlsberg B
Danske bank
DSV
Genman
Novo nordisk B
Novozymes B Vestas wind system
Coloplast B
Denmark 8
Fortum oyj
Kone oyj
Neste oyj
Sampo oyj
Storaensooyj
UPM
Finland 6
4.5 Variables
The key variables used in the analysis include risk-free rate, average annual
return, standard deviation of returns (Total risk), beta, unsystematic risk,
CAPM return, and Jensen alpha.
29
4.5.1 Risk-Free Rate
This is the return on riskless assets. The risk-free rate is important in this
study since it is used in the determination of CAPM required rate of return.
The yield of government bonds represent the risk-free rate. In this study, the
yield on 10-year Finland government bond is taken as the proxy for risk-free
rate. As on 27 October, the yield on 10-year bond was 0.138% (World
Government Bonds 2019). The annualized risk-free rate is determined as
follows:
Annualized Rf = (1 + 0.138%)250 - 1 = 3.51%
4.5.2 Return
Return is the percentage change in the daily close price of a stock. Daily
returns are calculated for each stock and the index as follows:
Daily return = (𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑑𝑎𝑦′𝑠𝑐𝑙𝑜𝑠𝑒 𝑝𝑟𝑖𝑐𝑒−𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑑𝑎𝑦′𝑠 𝑐𝑙𝑜𝑠𝑒 𝑝𝑟𝑖𝑐𝑒)
𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑑𝑎𝑦′𝑠 𝑃𝑟𝑖𝑐𝑒 × 100%
Annualized return = (1 + average daily return)250 – 1
4.5.3 Standard deviation (Total Risk)
Daily standard deviation of each stock and index is determined by the
following formula:
Daily Variance of stock returns, Var(r) = ∑ (𝑟𝑖 − 𝜇)2𝑛1
Daily Standard deviation = √𝑉𝑎𝑟(𝑟)
Annualized total risk (standard deviation) = Daily standard deviation × √250
4.5.4 Beta
Beta is the measure of systematic risk of stock relative to that of the market.
In this analysis, beta is determined through regression of each stock’s returns
and the index return. Beta is estimated for each of the 35 stocks.
Stock returns, Ri = α + βRm + є, Rm is the daily return on the market index
(OMX Nordic 40 Index). The slope of the market return in the model is the
estimate of the asset’s beta.
Given the values of beta and standard deviations, systematic and unsystematic
risk of each of the 35 securities are calculated as follows:
Total risk = standard deviation
30
Total systematic risk = Beta of the stock × standard deviation of index
(market)
Total unsystematic risk (residual variance) = Total risk – systematic risk
4.5.5 CAPM Return
CAPM return measures the required return based on a stock’s beta and the
market risk premium. It is calculated as follows:
4.5.6 Jensen Alpha
This is the difference between the actual and required return. Jensen alpha is
calculated using the formula below:
Jensen Alpha = Actual annualized Return – [Rf + Beta×(Rm – Rf)]
Table 2.4: Definition of Key variables
Name of variables Sources/Formula
Risk free rate www.worldgovernmentbonds.com/country/finland/
Return on stock Calculated from daily prices: (𝑃1 − 𝑃0)
𝑃0⁄
Return on OMX Nordic 40 Index Calculated from daily prices: (𝑃1 − 𝑃0)
𝑃0⁄
Equity beta (systematic risk) Slope of regression equation: Ri = α + βRm +є
Standard deviation of returns Calculated from daily prices √∑ (𝑟𝑖 − 𝜇)2𝑛
1
Total Systematic risk Beta × Standard deviation of index
Unsystematic risk (residual variance) Total risk – systematic risk
31
4.6 Data Analysis
Data analysis starts with the calculation of daily stock returns, and standard
deviation of returns. The average daily return is calculated for each of the 35
stocks for the whole period (2009 to 2019). The average returns and standard
deviation of the 35 companies are subjected to two stages of analysis. The first
stage is the time-series regression, while the second stage is the cross-sectional
regression. This is the same methodology applied by Miller, Jensen, and
Scholes (1972), Levy (1978), and Fama & MacBeth (1973), among other
empirical studies on CAPM.
4.6.1 Time-Series Regression
Regression analysis shows the relationship between two variables, a
dependent variable and independent variable (Lind, Marchal &Wathen 2019).
Linear regression assumes that there is a linear relationship between the
dependent variable and the independent variable. Linear regression model is
expressed as shown by the equation below:
Y = a + bX + є, where Y is the dependent variable while X is the independent
variable, and є is the error term. B is the coefficient of X and indicates the
change in Y (dependent variable) associated with a unit change in the
independent variable (Lind et al. 2019).
Time series regression is applied to estimate the beta of each stock. Time
series regression uses the daily returns of all the 35 stocks and index from
2009 to 2019. It is determined by regressing the returns on a stock against the
index return (Fabozzi, Rachev, Focardi & Hoechstoetter, 2013). In this case,
stock return is the dependent variable and the index return is the independent
or predictor variable (Lind, et al. 2019). The slope of the regression model
between the stock’s returns and the market return represents beta. The slope
of the model essentially shows the change in the stock’s return resulting from
a unit change in the index, or market return, which is synonymous with
systematic risk.
The calculated beta is then used to estimate the required return, total
systematic risk and unsystematic risk of each stock as follows:
Required return = Risk-free rate + Beta (Index return – Risk-free rate)
32
Jensen Alpha = Actual Annualized Return – CAPM required return
Total systematic risk = Beta × Standard deviation of index return
Total unsystematic risk = Standard deviation of stock – total systematic risk
The calculated values will be interpreted using descriptive statistics such as
mean, standard, minimum, and maximum. For instance, if the average Jensen
alpha of the 35 companies is positive, it would imply that the companies
outperformed the market.
4.6.2 Cross-Sectional Regression
According to Pardoe (2012), cross-section data is data gathered at one point in
time, unlike time-series data that is collected over a given period. In this study,
cross-sectional data was obtained by determining average return (10-year
average), standard deviation of the stocks’ returns, and beta for the entire
period (2009 to 2019). This gives a sample with 35 observations of average
return, standard deviation, and beta. Beta for each of the stocks was used to
calculate unsystematic risk or residual variance.
Two cross-sectional regression models are developed using Excel to test
CAPM. The first model is shows the relationship between beta and expected
return as shown by the equation below.
Y = α + β1Beta
Where: Y is the expected return (Average annualized return – Annualized risk-
free rate) and Beta is the systematic risk.
The objective of conducting cross-sectional regression is to determine the
relationship between stocks’ expected returns and risk. This helps in testing the
validity of CAPM by evaluating one fundamental assumption of CAPM, that
is, beta is the only significant variable influencing stocks’ returns (Fabozzi &
Ake 2013). For the regression model to meet the above assumption, it must
meet the following conditions:
1. The intercept of the model must be zero, that is, statistically
insignificant. Since CAPM assumes that beta is the only
determinant of return, the intercept of the regression model must be
equal to zero (Markowitz 2016). If the risk free rate is not deducted
33
from the stock’s actual returns, then the intercept of the model must
be equal to the risk-free rate for CAPM to hold. Thus, if the
intercept is statistically significant, it implies that beta is not the
only determinant of return (Lind, et al. 2019)
2. The coefficient of beta in the model must be statistically
significant. If the coefficient of beta is not statistically significant, it
implies that beta has no relationship with beta (Lind, et al., 2019).
This would suggest that beta is not a significant predictor of stock
returns, thereby invaliding the CAPM.
The model is interpreted using and t-tests of significance to determine if it
meets the above two conditions. They test the null hypotheses that the
intercept (α = 0) is zero, and that the coefficient of beta (β = 0) is zero (Pardoe
2012). Excel regression output indicates the p-values of intercept’s and
coefficient’s t-statistics. In this case, all tests are conducted at 5% significance
level. This implies that if the p-value is greater than 0.05, the null hypothesis is
not rejected (Pardoe 2012).
The R-square of the model shows the percentage of the variations in the
dependent variable (stock returns) explained by the predictor variable (Pardoe
2012). If the R square of the model is low, it indicates that beta is not the only
variable explaining stock returns. This would provide evidence against CAPM.
The second cross-sectional model is developed by adding residual variance or
unsystematic risk to the first model. The objective of developing the second
regression is to determine if the addition of residual variance improves the
model’s r square. If the r-square of the second model is greater than that of the
first model, it would indicate that beta is not the only determinant of return
(Markowitz 2016). Besides, this would imply that investors are compensated
for avoidable or diversifiable risk. The second model is shown by the
following equation:
Y = α + β1Beta + γRVar and RVar is the residual variance or unsystematic
risk.
34
4.6.3 t-Test for Difference in Means
The last statistical test is to determine if there have been significant changes in
systematic and unsystematic risk of the Nordic stocks in the last 10 years. In
this study, the average systematic and unsystematic risks of the 35 companies
in the first year 2009 (April 2009 to March 2010) is compared with the average
systematic and unsystematic risks in the last year (from April 2018 to March
2019).
To determine whether there has been a significant change, sample paired t-test,
also called dependent sample t-test, is conducted. Paired sample t-test is used
to assess whether there is a difference between the two samples(Lind et al.
2019). It tests the null hypothesis the means of the two samples are equal, that
is, the difference between the means is zero. According to Graham (2011),
paired sample test is used when the two samples are paired. This implies that
the samples come from the same population, and the only difference between
them is time. The two samples are paired since it is the same 35 stocks
measured in different periods; 2009/2010 and 2018/2019.
The test is conducted at 5% significance level. If the p-value of the t-statistic is
less than 5%, then there is a significant difference in the average systematic
and unsystematic risks between 2009/2010, and 2018/2019. If the p-value is
greater than 5%, then there is no significant change in risk.
Null hypothecs, H0: μ2009 = μ2019
Alternative hypothesis, HA: μ2009 ≠ μ2019
35
5. FINDINGS
5.1 Introduction
This chapter presents the results of data analysis and discusses the findings of
the study. It explains the results of time-series and cross-sectional regression
analyses and the implications of findings on the application of the CAPM to
the Nordic Stock Market. The time series regression is used to estimate the
stocks’ betas and determine Jensen Alpha, while the cross-sectional regression
analysis establishes the relationship between beta and stock average returns.
The results help determine whether it is appropriate for investors in the Nordic
Stock Market to apply CAPM in estimating expected returns. The chapter also
discusses the implications of the findings and compares them with previous
empirical studies on CAPM.
5.2 Descriptive Statistics
Time series regression was conducted using daily returns of 35 stocks selected
for the period between 2009 and 2019, to determine their betas. Average
returns and standard deviation of returns were calculated. The results are
presented as descriptive statistics in Table 3.1 below.
Table 3.1: Descriptive statistics
As shown in the above table, the average beta was 0.0191. This implies that
that systematic risk or volatility of the 35 stocks was about 99% lower than
that of the index. The maximum beta is 0.759, indicating that the systematic
risk of the most volatile of the 35 stocks, was 93% lower than the market
volatility. The minimum beta was -0.0246 suggesting that some stock returns
move in opposite directions to the movement of index returns.
The average CAPM return is 0.0364, implying that investors in the Nordic
stocks require a minimum annual return of 3.64% on their stocks.
BetaAnnualized
Return
Annualized
Standard
Deviation
Total
Systematic
Risk
Total
Unsytematic
Risk
CAPM
Return
Jensen
Alpha
Average 0.0191 0.1986 0.3164 0.0036 0.3128 0.0364 0.1622
Maximum 0.0759 0.9380 1.5866 0.0145 1.5721 0.0403 0.8978
Minimum -0.0246 0.0246 0.2059 -0.0047 0.2039 0.0334 -0.0127
36
5.3 Nature and Extent or Risk
Question 1- What is the nature and extent of risk in the last 10 years?
The total risk and the separation into systematic and unsystematic risk help
explain the nature and extent of risk in the Nordic Stock Market. As shown by
in Table 2 above, the average tot risk (standard deviation) is 0.3164 or 31.64%,
while the maximum total risk is 1.5866. Of this the average systematic risk is
0.0036 while the average total unsystematic risk is 0.3128. As shown in Figure
4 below, unsystematic risk constitutes 98.84% of the total risk of the 35 Nordic
stocks, while systematic risk accounts for only 1.16% of the total risk.
Figure 1: Composition of Total Risk
The composition of risk shows that most of the volatility of Nordic stock
returns is due to sector and firm-specific factors and not market-wide factors.
The high unsystematic risk can also be explained by the fact that the analysis
focused on individual stocks and not portfolios. Therefore, none of the
unsystematic risks has been diversified.
The study finds that more than 98% of the volatility of Nordic stock return is
due to unsystematic risk.
37
5.4 Jensen Alpha
Question 2- Has the Nordic stock market underperformed or outperformed
the expected return (CAPM) in the last 10 years?
This section answers the second research question. The actual return on the
stocks is compared with the CAPM required returns to assess whether they
have outperformed the market or not. The analysis shows that out of the 35
stocks, only two had negative Jensen alpha. 33 other stocks had positive
Jensen Alpha, implying that their actual returns exceeded the CAPM required
returns. The average Jensen Alpha is 16.22%, showing that on average, the
Nordic stocks outperformed the market by 16.22%. The maximum Jensen
alpha is 89%, indicating that the best performing stock delivered almost twice
the CAPM required return.
The analysis shows that the Nordic Stock market has outperformed the market
(expected return) in the last ten years between 2009 and 2019.
5.5 Findings of t-tests
Question 3- Is there any change in systematic, unsystematic and total risks
in Nordic stock market in the last 10 years between 2009 and 2019?
This section compares the stocks’ systematic and unsystematic risk between
2009 and 2019.
Table 3.2: t-test outputs
As shown in Table 3.2 above, the t-stat for the difference in systematic risk
between 2009 and 2019 is -10.125. The corresponding p-value is 0.000. The
2008/2009 2018/2019 2008/2009 2018/2019
Mean -0.000446419 0.00291486 Mean 0.023007689 0.01337127
Variance 1.66864E-06 1.80786E-06 Variance 4.55289E-05 1.13271E-05
Observations 35 35 Observations 35 35
Pearson Correlation -0.109547317 Pearson Correlation 0.280533334
Hypothesized Mean Difference 0 Hypothesized Mean Difference 0
df 34 df 34
t Stat -10.12539806 t Stat 8.583388882
P(T<=t) one-tail 4.23504E-12 P(T<=t) one-tail 2.50141E-10
t Critical one-tail 1.690924255 t Critical one-tail 1.690924255
P(T<=t) two-tail 8.47008E-12 P(T<=t) two-tail 5.00282E-10
t Critical two-tail 2.032244509 t Critical two-tail 2.032244509
UnSystematic RiskSystematic Risk
38
value is less than 5% implying that there is adequate proof to refute the null
hypothesis (Lind, et al., 2019). Therefore, it can be concluded that there has
been a significant change in systematic risk of Nordic stocks between 2009
and 2019 (Lind, et al., 2019). A comparison of the two means suggests that
systematic risk of the Nordic stocks has increased in the last ten years.
The p-value of the test of difference of unsystematic risk is 0.000. This
indicates that there is a significant difference between the mean of
unsystematic risk in 2009 and 2019. It implies that there has been a significant
change in unsystematic risk of Nordic stocks in the last years (Lind, et al.,
2019). The two means suggest that unsystematic risk has decreased in the
Nordic stock market.
5.6 Cross-Sectional Regression: Relationship between Risk and
Return
Question 4- What is the relationship between risk and return of stocks
listed on the Nordic Stock market?
5.6.1 Expected Return and Beta
The first cross-sectional regression model shows the association between
expected returns and beta. The model’s output is shown in Table 5.3 below.
Table 3.3: Regression model of returns and beta
The R Square (Coefficient of determination) of the model is 0.09991. It
implies that variations in beta of the 35 stocks explain only 9.991% of the
Regression Statistics
Multiple R 0.316088818
R Square 0.099912141
Adjusted R Square 0.072636751
Standard Error 0.149161505
Observations 35
ANOVA
df SS MS F Significance F
Regression 1 0.081500601 0.081500601 3.663087573 0.064336528
Residual 33 0.734222099 0.022249155
Total 34 0.815722701
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 0.150765856 0.031819942 4.738093299 3.98282E-05 0.086027696
Beta 1.943977768 1.015705124 1.913919427 0.064336528 -0.122489844
39
variations in actual returns on the stocks between 2009 and 2019 (Pardoe
2012). It suggests that beta explain a small percentage of the variations in
stock returns. More than 90% of the variations in stock returns is explained by
variables other than systematic risk. The model’s coefficient of determination
is small implying that its predictive power is low (Pardoe 2012). This indicates
that the model is not a good predictor of actual daily returns on stocks trading
on the Nordic Stock Market.
To determine if beta was the only determinant of the actual daily stock returns
of the 35 companies listed on the Nordic Stock Exchange, the intercept of the
model was tested for significance. The intercept of the model is 0.1508
suggesting that the average return on a stock would be 15.08% if beta is zero,
that is if systematic risk is zero (Pardoe 2012). The significance of the
intercept is determined by testing the null hypothesis that it is zero or
significantly close to zero. The t-statistic of the intercept is 4.738 with a p-
value of 0.0000398. The p-value is less than 5%, indicating that there is
sufficient proof to reject the null hypothesis. This implies that the claim that
the intercept of the model is zero or significantly close to zero is false.
Therefore, it can be concluded that the intercept of this model is not equal to
zero. The implication of the results is that the intercept is statistically
significant, meaning that beta is not the only determinant of actual returns on
stocks listed on the Nordic Stock Market (ibid.)
The coefficient of beta in the above model is 1.944 suggesting a positive
association between beta and actual daily returns on stocks listed on the Nordic
Stock Market (Graham 2011). It implies that a unit increase in beta (systematic
risk) is associated with an increase in the actual return by 1.944. This appears
consistent with the CAPM, which argues that higher systematic risk attracts a
higher return since investors require a high return to compensate for the high
risk. The t-statistic of the coefficient of beta is 1.914, and the corresponding p-
value is 0.0643. The p-value is higher than 0.05 implying that there is
inadequate evidence to reject the null hypothesis that the coefficient is zero
(Graham 2011). This means that the slope of beta is not statistically
significant. That is, beta has no significant association with actual stock
returns.
40
5.6.2 Expected Return, Beta, and Residual Variance
A second model was developed by adding residual variance. Residual variance
represents unsystematic risk. The model shows the relationship between
expected returns on the stocks and the two types of risks.
As shown in Table 5, the R square of the model is 0.7338, indicating that
systematic and unsystematic risk explained 73% of the variations in stock
returns of the 35 Nordic stocks. The value also implies that about 27% of the
variations in stock returns are due to factors other than systematic and
unsystematic risk (Pardoe, 2012). This suggests that risk is not the only
determinant of actual returns of Nordic stocks.
The square of this mode is higher than that of the model with beta as the only
predictor variable. It indicates that when residual risk is added to the equation,
its predictive power increases. This implies that CAPM does not hold.
Table 3.4: Regression model of returns, beta and residual variance
The intercept of the model is 0.0004, and the probability of its t-statistic is
0.8433. This is greater than 5%, meaning that it is not statistically significant
(Graham 2011). However, the coefficient of this Beta in the model is -0.12
suggesting a negative association between expected returns and beta. It
suggests that stocks that have high systematic risks are associated with lower
returns than those with low systematic. This is a violation of CAPM and
finance theories. The p-value of the t-statistic of the coefficient of beta is
Regression Statistics
Multiple R 0.856650311
R Square 0.733849755
Adjusted R Square 0.717215365
Standard Error 0.082368227
Observations 35
ANOVA
df SS MS F Significance F
Regression 2 0.598617904 0.299308952 44.11642033 6.33913E-10
Residual 32 0.217104797 0.006784525
Total 34 0.815722701
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 0.004831289 0.02425204 0.199211641 0.843357616 -0.044568501
Beta -0.12327414 0.608814909 -0.20248213 0.840821714 -1.363389527
Unsystematic risk 0.592878692 0.067909577 8.730413515 5.62791E-10 0.454551409
41
0.8408. This is greater than 0.05, indicating that beta has no significant impact
on actual returns (Graham 2011). On the other hand, the p-value of the t-
statistic of the slope of unsystematic risk is 0.000, implying that it is
statistically significant. Therefore, only unsystematic risk (residual risk) has a
significant impact on actual returns.
Therefore, from the above analysis, two conclusions can be seen. First, the
intercept is statistically significant implying that there are other significant
influencers of actual stock returns other than the stocks’ systematic risk (beta).
Secondly, the coefficient of beta is not statistically significant suggesting that
beta did not have a significant association with actual returns of the 35 stocks
listed on the Nordic Stock Market between 2009 and 2019. The results are a
violation of the CAPM which asserts that the return on an asset is dependent
on its systematic risk (beta). Thus, the CAPM was not valid for stocks listed on
the Nordic Stock Market between 2009 and 2014. The findings of this study
imply that CAPM is not accurate and should not be used in estimating the
required returns of Nordic stocks. The results are consistent with the findings
of Miller, et al. (1972), Levy (1978) and Östermark (1991), who found that
beta is not a good predictor of stock returns. Miller, et al. (1972) found that
beta explained only 21% of the variations in stock returns, and that is not
statistically significant. When residual variance was added to the model, the R
squared increased (Miller, et al. 1972). In this analysis, the addition of residual
variance increased the model’s R square from 9% to 73%.
5.7 Chapter Summary
This chapter presents the results of data analysis to assess the relationship
between returns and risk, and to test the validity of CAPM in the Nordic stock
market. The first objective was to determine the nature and extent of risk.
Returns and standard deviations were calculated, and time-series regression
used to estimate beta for each stock was estimated. Analysis of risks indicates
that 98% of the total volatility of stock returns was accounted for by
unsystematic risk, with systematic risk accounting for less than 1.5% of the
volatility of stock returns. Jensen Alpha indicated that the 35 stocks
outperformed the market (required returns). Only two of the 35 stocks had
negative Jensen Alpha. T-tests for the differences in systematic and
42
unsystematic risk between 2009 and 2019 rejected the respective null
hypotheses, implying that there was a significant change in both systematic
and unsystematic risk in the last ten years.
The validity of the CAPM was tested using two cross-sectional regression
models as applied by Miller et al. (1972) and Levy (1978). The first model
showed that there is no significant association between beta and actual returns.
The model’s R square indicated that beta explained only 9% of the variations
in actual returns of Nordic stocks. Significance tests of the model further
suggested that the intercept was statistically significant, implying that beta is
not the only determinant of returns. Besides, beta is not statistically significant
suggesting that systematic risk has no significant impact on Nordic stock
returns. When residual variance was added, the model’s R square increased to
73%, thereby rejecting the claim that only beta determines stock returns. Beta
was not statistically significant in the second model, while residual variance
(unsystematic risk) was statistically significant. These findings provide
evidence against the validity of CAPM in the Nordic stock market. The results
were consistent with previous empirical studies by Miller et al. (1972) and
Levy (1978) who used the same methodology and concluded that CAPM is not
valid.
6. CONCLUSION AND RECOMMENDATION
6.1 Conclusions
The study has focused on CAPM and its significance in estimating the returns
of investments. The study aim was to determine the performance of the Nordic
stock market over a ten-year period between 2009 and 2019. The study had
two main questions, which were set as follows: Is there any change in
systematic risk in between 10 years in Nordic stock market?And does the
Nordic stock market underperformed or over performed in 10 years? The
concept of CAPM has been seen to have originated in the mid-20th century,
after which interest continued to grow over the decades. As the concept grew
more popular, it attracted the interest of scholars and other researchers, and in
time, several studies were made which tested the underpinning theory of the
model as well as evaluated its effectiveness in predicting performance.
Theoretical concepts associated with CAPM include return and rate of return,
43
risk (both systematic and unsystematic), diversification of investment
portfolios and beta, which affects the market as a whole.The study combined
these concepts in the formula
Ra= Rrf + [β * (Re – Rrf)] where,
”Ra” denotes expected return on the security,
”Rrf” denotes risk free rate,
”β” denotes beta,
”Re” denotes expected return of market,
(Re – Rrf) denotes risk premium
Using this formula, the study relied on secondary data gathered from the
Nasdaq Nordic andsampled 35 companies. From the study, it was found that
CAPM is not useful in predicting the performance of Nasdaq Nordic. The
study also found that the findings are consistent with the previous findings
which also reached the conclusion that CAPM is not useful in predicting
performance of stocks in a market.
6.2 Summary and Discussion
From the descriptive statistics, it was found that the average beta was 0.0191,
while the maximum beta was 0.759. What this implies is that the selected
Nordic stocks had a systematic risk of 99% lowerthan the index.Further, the
Jensen Alpha analysis showed that the Nordic stock has outperformed the
market’s expected return based on CAPM productions. Looking at the t-test
values, there has been a significant change in the systematic risk in Nordic
stocks, and at the same time, there has been a significant change in the
unsystematic risk of this market. These findings are in line with the findings of
various previous studies, including those of Pardoe (2012) and Lind et al.
(2019) both of whom also reached similar conclusions.
CAPM is one of the most commonly used models in estimating returns on
investment. The model is applied in calculating the cost of capital, which is
critical in evaluating and appraising long-term investment decisions such as
the acquisition of fixed assets, expansion, among other capital budgeting
decisions. CAPM assumes that investors base their investment decisions on
44
risk and return. It shows the relationship between risk and return. The model
assumes that investors can establish efficient portfolios and diversify all
unsystematic risk. Therefore, only systematic risk should be considered in
estimating returns. Since the fundamental premises of CAPM is the risk-return
relationship, it is essential to understand the relationship between risk and
return to make sound investment decisions. This study analyzed data of 35
stocks listed on the Nordic stock markets to determine the nature and extent of
risk, and to tests whether both systematic and unsystematic risks have changed
over the last ten years. It also tested the validity of CAPM using cross-
sectional regression. Analysis of data suggests that unsystematic risk
constitutes about 98% of the total volatility of returns on Nordic stock markets.
Jensen alpha was used to compare actual performance to the required returns,
and found that the Nordic stocks outperformed the market or their required
returns. Tests of difference in samples indicated that there was a significant
change in both systematic and unsystematic risk of Nordic stocks between
2009 and 2019.
Cross-sectional regression was used to determine the association between risk
and return. In the model between returns and beta, it was found that beta is not
statistically significant and explained only 9% of the variations of actual
returns on the stocks. When residual variance was added to the model, the R
square increased to 73%. Only residual variance was found to be statistically,
with beta not having a significant effect on returns. The data seem to reject the
validity of CAPM in the Nordic stock market. The findings were similar to
those of Miller et al. (1972) and Levy (1978) who concluded that CAPM is not
valid.
The implication of the findings is that investors in the Nordic stock markets
should not rely on CAPM for estimating returns, especially when dealing with
individual stocks. CAPM is not valid and not reliable for estimating returns as
the study provides evidence against the validity of its assumptions.
45
6.3 Limitations of the Study
The study analyzed betas and returns of stocks and not portfolios. The CAPM
assumes that investors can eliminate all unsystematic risk by diversifying their
portfolios. The study used individual stocks, implying that no unsystematic
risk was diversified. With only 35 stocks, it was not possible to create
adequate sample of portfolios to test CAPM. This may have affected the
relationship between risk and return. According to Roll (1977), CAPM
presupposes that the index used in determining beta is efficient. In this study, it
was assumed that the OMX Nordic 40 Index is efficient. This is not realistic
since there can never be perfectly efficient markets in real life. Roll (1977)
further argue that CAPM is forward-looking since it determines expected
returns. Therefore, the use of historical data in testing CAPM can be
misleading.
6.4 Recommendations for Future Research
Based on the study, three recommendations are given. First, it is recommended
that investors in the Nordic stock markets should not rely on CAPM for
estimating returns, especially when dealing with individual stocks. The reason
is that CAPM is not valid and not reliable for estimating returns. The findings
of this study have shown that CAPM is not a valid measure for investors
because the beta did not have a significant association with actual returns of
the 35 stocks listed on the Nordic Stock Market between 2009 and 2019.
Further, any links between CAPM and returns were found to be insignificant,
and this is consistent with the previous findings in some of the studies cited in
the literature.
Secondly, it is also recommended that the managers should consider other
alternative models that predict the performance of organisations other than the
systematic and beta proposed in CAPM. One suggestion is using Multi Beta
Models. Unlike CAPM, which uses a single beta, multi-beta models use
various market risks, thus having more than one beta to predict risk. The
proposed models are the Arbitrage Pricing Model and The Multifactor model.
Thirdly, this study had a number of limitations, the main one being that it
focused primarily on the Nordic stock market but used a small sample size.
46
Thus, it is recommended that future studies look at a larger dataset within this
market to offer a supporting study that can confirm or contrast these findings.
Further, future studies on CAPM should develop efficient portfolios to test the
validity of CAPM. This will, ensure that all unsystematic risk is diversified
thus giving accurate estimates of beta. Besides, studies should focus on
identifying efficient portfolios for proxies as the market return. As outlined by
Roll (1977), if the benchmark is not efficient then the estimates of beta would
not be accurate.
47
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Appendix
Appendix 1. Information of Swedish companies
Serial
Number.
Name of
companies
Industry Website
1 ABB LTD Industrial http://www.abb.com
2 Alfa Laval Industrial http://www.alfalaval.com
3 Assa Abloy B Industrial https://www.assaabloy.com
4 Atlas Copco A Industrial http://www.atlascopcogroup.com
5 Astrazeneca Healthcare http://www.astrazeneca.com
6 Boliden Basic materials http://www.boliden.com
7 Electrolux B Technology https://www.electroluxgroup.com
8 Ericsson B Technology http://www.ericsson.com
9 Hexagon B Technology http://www.hexagon.com
54
10 Hennes &
Mauritz B
Consumer
Cyclical
http://www.hm.com
11 Investor B Financial
services
http://www.investorab.com
12 Nordea Bank
ABP
Financial
services
http://www.nordea.com
13 Sandvik Industrial http://www.sandvik.com
14 SEB A Financial
services
http://www.seb.se
15 SV.
Handelsbanken
A
Financial
services
http://www.handelsbanken.se
16 SKF B Industrial http://www.skf.com
17 Swedbank A Fiancial
services
55
18 Swedish Match Consumer
Defensive
http://www.swedishmatch.com
19 Tele2 B Communication
services
http://www.tele2.com
20 Telia Company Communication
services
http://www.teliacompany.com
21 Volvo B Industrials http://www.volvogroup.com
56
Appendix 2- Information on Denmark companies
Serial
Number
Name of
companies
Industry Website
1 Carlsberg B Consumer
Defensive
http://www.carlsberggroup.com
2 Danske Bank Financial
services
http://www.danskebank.com
3 DSV Panalpina Industrial http://www.dsv.com
4 Genmab Healthcare http://www.genmab.com
5 Novo Nordisk
B
Healthcare http://www.novonordisk.com
6 Novozymes B Basic materials http://www.novozymes.com
7 Vestas Wind
System
Industrial http://www.vestas.com
8 Coloplast B Healthcare http://www.coloplast.com
57
Appendix 3- Information on Finnish Companies
Serial
Number
Name of
companies
Industry Website
1 Fortum Oyj Utilities https://www.fortum.com
2 Kone Oyj Industrial http://www.kone.com
3 Neste Oyj Energy https://www.neste.com
4 Sampo Oyj A Financial
services
http://www.sampo.com
5 Stora Enso Oyj R Basic Material http://www.storaenso.com
6 UPM-Kymmene
Oyj
Basic material http://www.upm.com
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